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The vertex form of the given equation is (x - 9/2)² - 1/4

Vertex form

The general vertex form is written as

y = a (x - h)² + k

Where, a, h, and k are real numbers, where a ≠ 0.

And x and y are variables where (x, y) represents a points.

Given,

Here we have the equation x² = 9x - 20

Now, we have to convert this equation into vertex form.

In order to convert this into vertex form, first we have to rewrite the given equation as follows:

=> x² - 9x + 20 = 0

Here the coefficient of the x is 9, so now we divide this by 2 : 

=> 9 ÷ 2 = 9/2

And then we have to square it (9/2) ² then we get the value 81/4.

So we add and subtract 81/4, then we get,

=>  x² - 9x + 81/4 - 81/4 + 20 = 0

Now, we have to rewrite it as,

=> [x² - 9x + 81/4] + [-81/4 - 20]

When we simplify it then we get,

=> (x - 9/2)² - 1/4

Therefore, the vertex form of the equation is  (x - 9/2)² - 1/4.

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Answer:

[tex]0.2[/tex]

Step-by-step explanation:

... .. ... .. .

When corresponding angles are congruent, the lines are parallel

Congruent angles are two or more angles that are identical to each other. Thus, the measure of these angles is equal to each other. The type of angles does not make any difference in the congruence of angles, which means they can be acute, obtuse, exterior, or interior angles. The angles which occupy the same relative position at each intersection where a straight line crosses two others. If the two lines are parallel, the corresponding angles are equal.

Examples of the corresponding angle are any angles which are formed on the opposite side of the transversal. Now, it should be noted that the transversal can intersect either two parallel line or two non-parallel lines. Thus, corresponding angles can be of two types:

Corresponding angles formed by parallel lines and transversals

Corresponding angles formed by non-parallel lines and transversals

Looking at the image, angle I is congruent to each other. Angle II is congruent with each other as well as angle III.

When corresponding angles are congruent, the lines connecting them must be parallel. This is the only valid or correct options in the task.

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Answer:

[tex]f(x) = 2(x-9)^{2} + 3[/tex]

Step-by-step explanation:

In vertex form, (h, k) represents the vertex.

With the given vertex of (9, 3), h = 9 and k = 3. You can substitute those values into the equation.

In vertex form, a represents vertical stretch or compression.

In this case, since the parent function, x^2 is multiplied by 2, a = 2. You can substitute this into the equation.

You end up with [tex]f(x) = 2(x-9)^{2} + 3[/tex]

By 6 months both of them have same amount

Each of them have $700 at that 6 months.

In French, an equation is defined as having one or more variables, whereas in English, an equation is any well-formed formula consisting of two expressions linked by an equals sign.

Unknowns are the variables for which the equation must be solved, and equation solutions are the values of the unknowns that satisfy the equality.

Given that, Erlena has $250 and she saves $75/month then,

The equation is,

250+75x

And also given that, Jabril has $400 and he saves $50/month then,

The equation is,

400+50x

250+75x=400+50x

150=25x

x=6

By 6 months they have same amount

250+75(6)=700

400+5(6)=700

They both have $700 at that 6 months

Therefore, By 6 months both of them have same amount

Each of them have $700 at that 6 months.

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The probabilities, using the Poisson distribution, are given as follows:

a) Two earthquakes in a year: 0.0446 = 4.46%.

b) No earthquakes in two consecutive months: 0.3679 = 36.79%.

c) No earthquakes in two consecutive months, given that there were no earthquakes in the previous month: 0.3679 = 36.79%.

The Poisson distribution is used when we only have the mean in a given interval and the mass function is given as follows:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

The parameters are listed as follows:

For one year, the mean number of earthquakes is given as follows:

[tex]\mu = 6[/tex]

The probability of exactly two earthquakes in a year is obtained as follows:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 2) = \frac{e^{-6}6^{2}}{(2)!} = 0.0446[/tex]

For two months, the mean is given as follows:

[tex]\mu = 2 \times 6 \times \frac{1}{12} = 1[/tex]

For items b and c, the probabilities are the same, P(X = 0), as the events are independent, hence:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-1}1^{0}}{(0)!} = 0.3679[/tex]

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The value of the expression when m = 3 is 13/15. So option(2) is correct.

The equation is defined in its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, x + 3 = 4 is an equation, in which x + 3 and 4 are two expressions separated by an 'equal' sign.

Given the expression as shown below:

2/5 m - 1/3

If m is equal to 3, then the expression will be;

2/5(3) - 1/3

6/5 - 1/3

Find the LCM

6/5 - 1/3 = 3(6)-5/15

6/5 - 1/3 = 18-5/15

6/5 - 1/3 = 13/15

Therefore the value of the expression if m = 3 is 13/15

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Step-by-step explanation:

Rigid motion

Rigid motion – A transformation that preserves distance and angle measure (the shapes are congruent, angles are congruent).

Answer: Minimum cost = $264

Paint left over = 7/8 qt

Step-by-step explanation:

6 gal covers 1920 sf (6 gal x 320 sf/gal)

6 gal x $29/gal = $174

2250 sf - 1920 sf = 330 sf

Need 4.125 qt to cover 330 sf, but you can't buy a partial quart

5 qt x $18/qt = $90

Total cost = $174 + $90 = $264

You have 7/8 qt left over

The y-intercept (0, 1200) represents the initial cost of the bedroom furniture option (A) is correct.

It is defined as a function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent y = a×

where a is a constant and a>1

The exponential function is of the form:

y = ab×

Plug x = 0 and y = 1200

1200 = a

Plug x = 2, y = 675, and a = 1200

675 = 1200(b)²

b = 0.75

y = 1200(0.75)×

y = 1200

Thus, the y-intercept (0, 1200) represents the initial cost of the bedroom furniture option (A) is correct.

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Amount of $150,000 represents 42.86% of $350,000.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have Danny’s home cost $350,000. The federal government program for flood damage insurance covers only $150,000.

Assume that it represents [x%] percent of the total value. Then, we can write -

x = (150000/350000) x 100

x = 42.86%

Therefore, $150,000 represents 42.86% of $350,000.

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The trinomial and binomial form of the incomplete algebraic expression is [tex]d^{2}[/tex] -3d + 9/4 and [tex](d-\frac{3}{2}) ^{2}[/tex]

A perfect square is a quadratic expression that factors into two identical binomials.

For example, if you multiply these two identical binomials factors:

(x + 2)(x + 2)

to complete the square in the expression [tex]d^{2}[/tex] -3d, we square the half of the coefficient of d which is -3/2

so the expression becomes,

[tex]d^{2}[/tex] -3d + [tex](\frac{-3}{2}) ^{2}[/tex] = [tex]d^{2}[/tex] -3d +[tex]\frac{9}{4}[/tex]

The Binomial form of the expression [tex]d^{2}[/tex] -3d + [tex](\frac{-3}{2}) ^{2}[/tex]

can be written by take [tex]d^{2}[/tex] term and the constant and putting them in a bracket and squaring

which becomes

[tex](d - \frac{3}{2} )^{2}[/tex]

In conclusion, the trinomial form of the expression is [tex]d^{2}[/tex] -3d +[tex]\frac{9}{4}[/tex] while the Binomial form of the expression is [tex](d - \frac{3}{2} )^{2}[/tex]

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Option (C) is the correct one and the only true statement is

The domain of the function f(x) is { -2, -1, 0, 1, 2, 3, 4, 5, 6 }.

Given, a table of values for y = f(x)

x     -2   -1   0   1   2   3   4   5   6

y      7   8   9   10  11  5   6  12  13

We have to find the correct statements,

as the range of the function f(x) is { 4, 8, 9, 10, 11, 5, 6, 12, 13 }

the image of 5 in the function is 6 i.e. f(5) = 6.

The domain of the function f(x) is { -2, -1, 0, 1, 2, 3, 4, 5, 6 }

the image of -1 in the function is 8 i.e. f(-1) = 8.

Hence, only the option (C) is the correct one and the only true statement is

The domain of the function f(x) is { -2, -1, 0, 1, 2, 3, 4, 5, 6 }.

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The speed of slower bus is 118 km/hr and speed of faster bus is 133 km/hr

Speed is a scalar quantity that refers to "how fast an object is moving".

Given that, two buses leave a station at the same time and travel in opposite directions, one bus travels 15 km/h faster than the other, the two buses are 1004 kilometres apart after 4 hours,

Speed = distance/ time

Let the speed of the slower bus be v and the faster bus be (v+15)

According to the question,

vt + (v+15)t = 1004

vt + vt + 15t = 1004

t = 4

4v + 4v + 60 = 1004

8v = 944

v = 118

Hence, The speed of slower bus is 118 km/hr and speed of faster bus is 133 km/hr

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Using the mathematical operation of subtraction, the cost at Fast BMX is $200 more than the cost at Bike World.

The difference in the cost of bikes can be computed using the mathematical operation of subtraction.

Subtraction operations involve deducting the subtrahend from the minuend to get the result known as the difference.

Bike Stores              Prices

Bike City                   $300

Fast BMX                 $500

Bike World               $300

Awesome Bikes      $400

Difference between Fast BMX and Bike World

= $200 ($500 - $300)

Thus, the cost of bikes is higher at Fast BMX than at Bike World by $200.

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Answer: x= p16

Step-by-step explanation:

The probability is 0.00332.

From the given question,

Danny Nguyen has A 7 and opponent has A K+.

The flop is : 5 K 5

As there are two players playing the remaining cards in the deck will be (52 - 2 - 2 - 3 -1(burn)) = 44

For Nguyen to win he needs two of the three 7's left in the deck for turn and river.

For turn we have to select a 7 from the three 7's and for river we have to select a 7 of the remaining two 7's.

So the probability is

P = [tex]\frac{\binom{3}{1}}{\binom{43}{1}}*\frac{\binom{2}{1}}{\binom{41}{1}}[/tex]

P = 0.00332

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Answer:

27

Step-by-step explanation:

I looked at the graph and added 6+6=12 so the bottom is 12 and for the height i added 1+8=9 and then i added another 12 because the bottom is also 12 and divided that by 2 which is 6 so i got 27.

this may not be right but i am hoping that is it!

Have A Great Day!!!

Answer:

?????

Step-by-step explanation:

Answer:

Step-by-step explanation:

Quadratic equation:

Substitute p and q:

Find the value of a, using the y-intercept:

The equation is:

or

Answer:

72.1

Step-by-step explanation:

It is 10 to the power of 2 because the exponent is 2. The result is a number bigger than the origin or base number because the exponent is positive. We move the decimal two times to the right to arrive at our conclusion:

0.721--> 72.1

therefore, your answer will be 72.1

The total profit that the company would make on the trip can be found to be £7,320

The revenue that the company makes would be:

= Number of passengers x Amount that each passenger pays

= 400 x 23

= £9, 200

Each coach takes 50 passengers so the number of coaches needed are:

= 400 passengers / 50 passengers per coach

= 8 coaches

The total cost to the company for the trip is:
= (Number of coaches x Driver cost per coach) + (Number of coaches x Fuel per mile x Distance traveled for each coach)

= ( 8 x 95) + ( 8 x 70p x 200)

= 760 + 112, 000 p

= 760 + 112, 000/ 100 pence per pound

= £ 1,880

The total profit is:

= Revenue - total cost

= 9, 200 - 1, 880

= £7,320

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Answer:

70 km/hr

Step-by-step explanation:

The function on the graph can't be a sin, then the correct option is:

y = A*cos(k*x) + C

We know that the graph is either of the equation:

y = B*sin(k*x) - C

Or

y = A*cos(k*x) + C

Now, notice that there is a maximum at x = 0

And we also know that:

sin(0) = 0

cos(0) = 1

Then the option with the sin can be discarded, as it does not have a maximum at x = 0.

The correct option is:

y = A*cos(k*x) + C

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The image of (3, 3) after dilation  by a scale factor of 1/3 centered at the origin will have coordinate (1, 1)

Dilation refers to the transformation that increases or reduces the image formed after the transformation

When the scale factor is greater that 1 the transformation will lead to magnification when the scale factor is less than 1 the image formed is compressed.

The transformation rule fir dilation is (x, y) → (kx, ky)

where k is the scale factor = 1/3

(3, 3)  → (1/3 * 3, 1/3 * 3)  → (1, 1)

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Answer:

The second option so 54 degrees.

Step-by-step explanation:

The line drawn on angle d in both spots indicates it's congruent so if one side is a number the other side is that same number so in this case, it's 54 degrees.

Answer:

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